Use the Pythagorean Theorem to determine the missing side of the following right triangle.

Answer

The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this triangle, the sides forming the right angle are 9 and the missing side, x. The hypotenuse is the longest side, which is 40. Therefore, we can write the equation according to the Pythagorean Theorem: 9^2 + x^2 = 40^2. Calculating the squares, we get 81 + x^2 = 1600. To solve for x^2, we subtract 81 from both sides of the equation: x^2 = 1600 - 81. This gives us x^2 = 1519. To find the value of x, we take the square root of both sides: x = \( \sqrt{1519} \). To find the numerical value of \( \sqrt{1519} \), we can use a calculator. \( \sqrt{1519} \approx 38.97435 \). Rounding to a reasonable number of decimal places, we get x \( \approx \) 38.97. So, the missing side x is approximately 38.97 units.